Holomorphic triples and the prescribed curvature problem on $S^2$
Differential Geometry
2015-03-20 v1
Abstract
We prove new results on existence of solutions for the prescribed gaussian curvature problem on the euclidean sphere S^2. Those results are achieved by relating this problem with the holomorphic triples theory on Riemann surfaces. We think this approach might be applied to study some other semi-linear elliptic equations of 2nd order on the sphere.
Keywords
Cite
@article{arxiv.1503.05886,
title = {Holomorphic triples and the prescribed curvature problem on $S^2$},
author = {Alexandre C. Gonçalves},
journal= {arXiv preprint arXiv:1503.05886},
year = {2015}
}